On this page you will find resources relating to the teaching and learning of geometries, including Euclidean geometry, coordinate geometry, and transformation geometry.
1. Development of Geometric Thought: Van Hiele Levels (Visualization, Analysis, Informal Deduction, Deduction, Rigor)
4. Tangrams are not Toys!
Reasoning with Tangrams by finding the underlying structure through a folding activity: Download (PDF)
5. Proving
a. The November 2009 issue of the NCTM journal The Mathematics Teacher is entirely devoted to proving: LINK
b. An article I wrote regarding informal deductive reasoning in sixth graders: Download (PDF)
c. The Travel Metaphor: Download (PDF)
d. Three columns instead of two, a strategy to help students with proving: Download (PDF)
Teacher examples: Example 1Example 2 (DOC) Using Educreations to study facial symmetry LINK
On this page you will find resources relating to the teaching and learning of geometries, including Euclidean geometry, coordinate geometry, and transformation geometry.
1. Development of Geometric Thought: Van Hiele Levels (Visualization, Analysis, Informal Deduction, Deduction, Rigor)
For detailed explanations: Download (PDF)
2. Classifying quadrilaterals: Go Fly a Kite!
We classify quadrilaterals by reasoning with their diagonals: Download (PDF)Geogebra files: one-bisect-congruent one-bisect-not-congruent two-bisect-congruent two-bisect-not-congruent
CCSS controversy: Inclusive versus exclusive definition of a trapezoid
3. Pythagoras: Reasoning about the relationship of areas of squares on sides of triangles.
Tile Activity: Download (DOCX)Tile Squares for Tile Activity: Download (DOCX)
Geogebra File: Pythagorean Relationships of triangles 1
Geogebra File: Pythagorean Relationships of triangles 2
Geogebra File: Pythagorean Relationships of Triangles 3
Liquid "Proof" (YouTube): LINK
Visual Proof (NCTM Illuminations): LINK
Animated proof (YouTube): LINK
Historical approach: Download (PDF)
Inquiry Lesson Video focused on AREAS: https://www.teachingchannel.org/videos/pythagorean-theorem-lesson
Inquiry Lesson Video focused on SIDES: https://www.teachingchannel.org/videos/teaching-pythagorean-theorem
4. Tangrams are not Toys!
Reasoning with Tangrams by finding the underlying structure through a folding activity: Download (PDF)
5. Proving
a. The November 2009 issue of the NCTM journal The Mathematics Teacher is entirely devoted to proving: LINKb. An article I wrote regarding informal deductive reasoning in sixth graders: Download (PDF)
c. The Travel Metaphor: Download (PDF)
d. Three columns instead of two, a strategy to help students with proving: Download (PDF)
- Teacher examples: Example 1 Example 2 (DOC) Using Educreations to study facial symmetry LINK
- GIP Template: Download (DOCX)
- Example assignment: Download (DOCX)
e. Proving and reasoning logically is not exclusive to Geometry. One example, Logic in the coordinate plane: Download (PDF)6. Proving Congruence and Similarity in the CCSS
Geogebra files:
Congruence Solution
Congruence 2 Solution
Similarity Solution
7. Common Core development of Geometry grades 6-12: Download (DOCX)
PARCC sample Geometry Questions: LINK8. Transformation Geometry
Rotation Lesson Study PLAN: DOWNLOADRotation Lesson Study WORKSHEET: DOWNLOAD
Composition of reflections: PARALLEL INTERSECTING
9. Longsword dancing and stable geometrical shapes (Video):
http://simonsfoundation.s3.amazonaws.com/jwplayer/longsword/Longsword-dancing-2b_compressed2.mp4